A cryptographic calculation includes obtaining a point P(X,Y) from a parameter t on an elliptical curve Y2=f(X) and from polynomials satisfying: −f(X1(t))·f(X2(t))=U(t)2 in the finite body Fq, irrespective of the parameter t, q=3 mod 4. A value of the parameter t is obtained and the point P is determined by: (i) calculating X1=X1(t), X2=X2(t) and U=U(t); (ii) testing whether the term f(X−1) is a squared term in the finite body Fq and, if so, calculating the square root of the term f(X1), the point P having X1 as abscissa and Y1, the square root of the term f(X1), as ordinate; (iii) otherwise, calculating the square root of the term f(X2), the point P having X2, as abscissa and Y2, the square root of the term f(X2), as ordinate. The point P is useful in encryption, scrambling, signature, authentication or identification cryptographic applications.
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2. Method of execution of a cryptographic calculation according to claim 1 , in which the following steps are executed at step /2/-/ii/: calculating R 1 such that: R 1 = f ( X 1 ) q - 1 2 if R 1 is equal to 1, deciding that the term f(X 1 ) is a squared term in field F q ; and calculating Y 1 = f ( X 1 ) q + 1 4 otherwise, calculating Y 2 = f ( X 2 ) q + 1 4
6. Method of execution of a cryptographic calculation according to claim 1 , in which, at step /1/, the value of the parameter t is obtained as a function of a password or an identifier.
7. Method of execution of a cryptographic calculation according to claim 1 , in which the cryptographic application is an application of authentication or identification by a checking entity, and in which, at step /1/, the following steps are executed: /a/ generating a random value; /b/ obtaining an encrypted value by encrypting said random value based on an encryption function using an encryption key determined from a password or identifier corresponding to the parameter; and /c/ transmitting the encrypted value to the checking entity.
Cooperative Patent Classification codes for this invention. Click any code to explore related patents in that topic.
June 15, 2010
April 29, 2014
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